WHAT would happen to our culture if children were completely cut off from their grandparents? In today's highly mobile, divorce-prone society, it's a serious question - one that anthropologist Margaret Mead, speaking at a public forum in the 1970s, called our ''most vital.'' Something special occurs between those two generations, sociologists note, creating a channel through which traditions are passed along and culture is learned.
''Parents are generally pretty busy people,'' writes Bess Lomax Hawes, director of the folk arts program of the National Endowment for the Arts. ''Even thinking about teaching a young child can be an added imposition, though most parents will 'shew' a thing or two on the fly. But the longer-term, more serious learning relationships generally skip a generation.''
As the dispenser of the Endowment's National Heritage Fellowships, Ms. Hawes has noticed a pattern among folk artists. All those granted fellowships so far have been over 50, she says - and most seemed to have learned their art from their own grandparents.
Where does that leave our children's generation? ''It is dismally true that within the contemporary United States, at least, changing patterns of housing, employment, and family structure have driven deep rifts into the vital communicative chain that has transmitted cultural values, skills, and morale across the generations from millennia,'' she says. ''It is a deeply troubling situation.''
The score of grandparents' rights organizations that have sprung up recently apparently share that feeling. One spokesman - Arthur Kornhaber, author of a book on the grandparent-grandchild connection and president of the Foundation for Grandparenting - dubs what he sees as a sharp decline in the three-generational family ''The New Social Contract.''
This ''dismemberment of the family,'' he believes, has led to a gradual abandonment of children, an increased willingness by family members to institutionalize each other, and the ''replacement of basic family functions by businesses and social institutions.''
While some members of such grandparents organizations may agree with Dr. Kornhaber's dire outlook, most seek simply to redress not the entire social structure, but a legality they consider to be a straightforward denial of rights - visitation rights between themselves and their grandchildren.
The million children involved in divorce each year often find themselves shut off from the parents of the noncustodial parent (and sometimes the custodial parent as well), these groups say, ''because of the hostilities between the divorcing couple who use the children as pawns, in an effort to get even with each other,'' according to one spokesman.
In what appears to be a national movement, 42 states have instituted laws that provide for grandparents' visitation under some circumstances, and three others are considering bills this year. The laws, says a spokesman from the Michigan-based Grandparents/Children's Rights Inc., range ''from good to very limited,'' and grandparents attempting to use them have often been stopped by a lack of reciprocity between the states.
Redressing this lack is the impetus behind a Grandparents Visitation Act, which passed the US House and has lain in the Senate Judiciary Committee since last spring. Sponsored by Carl Levin (D) of Michigan and 29 of his colleagues, the bill expresses the hope of the Congress that the National Conference of Commissioners on Uniform State Law (a nongovernmental body promoting uniformity in state laws) will develop a model grandparents visitation rights law that addresses reciprocity and allows all grandparents the right to petition the courts for visitation.
A spokesman from the National Conference, however, says the conference has decided against drafting such a law, since two laws drafted previously by them - covering child custody and adoption - already cover visitation rights (these laws are offered by the conference to statehouses to adopt or adapt as they please).
But the effort to gain these rights has apparently galvanized a number of groups and helped them to focus on what Ms. Hawes of the NEA calls the ''every-other-generational pattern,'' a grandparent-grandchild treasure making ''an infinitely subtle and effective communicative pattern that provides both for continuity and for change in proportions that are balanced with extraordinary delicacy.''
''Even in such mundane interactions as learning to make baking powder biscuits or how to tune a fiddle 'Sebastopol' style, the leitmotifs of 'Well, the way I always heard it' and 'But why couldn't it?' intertwine in a never-ending dance of give and take, stability and innovation,'' she writes.
''It is a great system,'' she believes, ''and I hate to see it weakening because half of the participants are in retirement villages and the other half have gone off to day camps.''
''Where would we all be if it were not for our own grandparents?'' asks Gerrie Highto, a grandparents' rights spokeswoman from Baltimore, Md., in hearings held by Congress last spring. ''There is no love that can replace the very special love of the grandchild and the grandparent, and how sad it is for the grandchild who never knew or does not remember his grandparents.
''Let us not forget,'' she concludes, referring to her grandchildren's generation, ''that we are their roots.''